What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.

Answers

Answer 1
Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}

Related Questions

Are the ratios 6:1 and 19:3 equivalent?

Answers

Answer: no<3

Step-by-step explanation:

leave a thanks if helped plz

Can someone please help me

Answers

Answer:

Answer for question 16 $24.64

Answer:

$3.36

17. 31%

18 $ 24.50

Step-by-step explanation:

28 x 0.12 = $3.36

17. 484 - 333.96 = 150.04

What percentage is 150.04 of 484

X/100 = 150.04/484 (% / 100 = is/of)

= 31%

8. 35 x 0.30 = 10.50

$35 - $10.50 = $24.50

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

If a submarine dives 378 feet in 14 seconds, the average change in elevation is feet per second.

Answers

Answer:

27 feet per second.

Step-by-step explanation:

You already have your time unit in second and length measurement in feet so just divide the two 378/14=27 feet per second.

Answer:

-27 feet per second

Step-by-step explanation:

378 ÷ 14 = 27

because the submarine is going down, the sign has to be negative

if f(x) = 7(x-1) + 8 , what is rhe value of f(11) ?​

Answers

Answer:

f(11)=78

Step-by-step explanation:

f(11)=7(11-1)+8

f(11)=77-7+8

f(11)=78

Answer:

F(11) = 78

Step-by-step explanation:

f(11) means that you would just have to replace “x” on the equation with 11 and then solve;

=> f(11) = 7(11 - 1) + 8

=> f(11) = 7(10) + 8

=> f(11) = 70 + 8

=> f(11) = 78

therefore the answe is 78

Hope this helps!

(9x+3)5 i really need help with this pleaseeee

Answers

Answer:

1/15

Step-by-step explanation:

Thats my guess I think its that though.

Answer: 3

Step-by-step explanation:

PEMDAS

Would you rather have 15/20 of a pizza or 3/4 of a pizza? Explain your answer and how you solved the problem. plz hurry!

Answers

they are both equal and are the same value(75%)

5. Use the point-slope formula to determine the equation of a line that passes through the points (1, 2) and (-2, 1).

Answers

Answer:

In point-slope form the equation is:

[tex]y - 2 = \binom{1}{3} \times (x - 1)[/tex]

Some students have a goal of collecting 200 leaves for a science
project. What does 0% of the goal mean in this situation? What does 100% mean?

Answers

Answer:

0% is none of the leaves and 100% is collecting all of them

In February Lana got a puppy that weighed 13 kilograms. By October the puppy weighed 16.9 kilogram. What was the puppy’s weight increase?.

Answers

16.9 minus 13 equals to 3.9 increase

Answer:

3.9

Step-by-step explanation:

16.9 take away 13 and you get 3.9 kilograms

3. If Superman can fly .25 miles in 8 seconds, how far could he fly in...
(a) 40 seconds?


Answers

Answer:

1.25 miles

Step-by-step explanation:

0.25 miles = 8 seconds

x miles = 40 seconds

0.25/8 = x/40

0.25 * 40 = 8x

10 = 8x

x = 1.25

-Chetan K

Body surface area is calculated a) in m2 from weight and height. b) from height. c) from weight. d) in meters from weight and height.

Answers

Answer:

Body surface area is calculated a) in m2 from weight and height.

Step-by-step explanation:

Basically the surface has to be in m2, because you have two dimensions when you multiply: e.g. when you have a lawn 10m x 10m, then you multiply 10 times 10, and meters times meters, so

[tex]10m * 10m = 100m^2[/tex]

What determines whether a relationship
is proportional or not?

Answers

Answer:

When two ratios exhibit the same connection, they are said to be proportionate. Two ratios may be tested for proportionality by writing them as fractions and then reducing them to the smallest possible number. In this case, your ratios are proportionate since the reduced fractions are the same.

Step-by-step explanation:

Hope it helps:)


John buys a computer on sale for $450.00. He
pays $50.00 less than have the original price. How
much was the original price of the computer?
Write and solve an equation

Answers

First you can add 50 dollars to 450 dollars which is 500 then divide that 500 by 2 and that is 250

Answer:

$450+$50= X

X=$500

Step-by-step explanation:

The sale price is $450.00, so you take that amount and $50.00 which the amount he paid less and add them both. We do this because we want to see the original price of the computer. If it mentioned the original price already and the amount $50.00 and asked the sail price instead, we would have to subtract to get the answer.

Here we have to add.

450+50=500

(add the dollar sign)

$450+$50=X

X=$500

Round any answers to the nearest tenth if necessary.
ad
Technology required. Find the
missing measurements.
nd
35
А.
21
B
BC is 40
I
units, degrees, and 60
degrees.

Answers

He’s gonna give u a link he did it to me and it didn’t work

5/12+2/3=37 I need help

Answers

Answer:

13/12=37

Step-by-step explanation:

e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.

Answers

Answer:

Step-by-step explanation:

4/50 = 0.08

0.08(100) = 8%

Pls help I need ASAP pls

Answers

Answer:

  -1

Step-by-step explanation:

The line goes down 1 grid square for each grid square to the right. Each grid square represents 1 unit in both the x- and y-directions. That means the slope is ...

  m = rise/run = -1/1 = -1

The slope of the line is -1.

when a company produces 5,000 units, variable costs are $35 per unit and total cost in $200,000. What is the total cost when the company produces 8,000 units? (both 8000 and 5000 units produced are within the relevant range.)

Answers

$320,000 is what the company produces with 8000 units.-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------


17) Which number is located the same distance on
a number line from -5 as 3 is?

Answers

Answer: -13

Step-by-step explanation:

I know that the distance between -5 and 3 is 8 so I subtracted 8 from the negative 5 so it would be the same distance and I got -13

Answer:

-13

Step-by-step explanation:

help me due today it is mathematics

Answers

Answer:

Miranda is correct because the value 7 makes the equation equal

I am not sure what goes in the blanks, those are my best guesses.

Step-by-step explanation:

34 = 27 + p

7 = p

Hopefully this helps!

Brainliest please?

regal furniture company allocates its indirect salaries of $22,500 on the basis of sales. Determine the indirect salaries allocated to Departments 1 and 2 using the following information.

Answers

Answer:

$15750 and $6750

Step-by-step explanation:

Revenue share of Dept. 1:

182000/260000*100% = 70%

Revenue share of Dept. 2:

100% - 70% = 30%

Allocate the indirect salary with same ratio.

Dept. 1:

22500*70/100 = 15750

Dept. 2:

22500 - 15750 = 6750

In the EXPLORE online library, the ratio of the number of novels to that of dictionaries is 2:3 and the total number of novels is 624. If Joe buys more novels and the ratio becomes 7:3, then how many novels have been bought in total?

Answers

Using a system of equations, it is found that 1530 more novels have been bought in total.

For the system, we have that:

x is the number of novels.y is the number of dictionaries.

The ratio of the number of novels to that of dictionaries is 2:3, hence:

[tex]\frac{x}{y} = \frac{2}{3}[/tex]

[tex]3x = 2y[/tex]

[tex]y = \frac{3x}{2}[/tex]

Total number of novels is 624, hence:

[tex]x = 624[/tex]

[tex]y = \frac{3}{2} \times 624 = 936[/tex]

Buys z more novels, and the ratio becomes [tex]\frac{7}{3}[/tex], hence:

[tex]\frac{624 + z}{923} = \frac{7}{3}[/tex]

[tex]1872 + 3z = 6461[/tex]

[tex]z = \frac{6461 - 1872}{3}[/tex]

[tex]z = 1530[/tex]

1530 more novels have been bought in total.

A similar problem is given at https://brainly.com/question/17096268

Mort and George are 18 miles apart on a path when they start moving toward each other. Mort runs at a constant speed of 7 miles per hour, and George walks at a constant speed of 5 miles per hour. How long does it take until Mort and George meet?

Answers

Answer:

  1 1/2 hours

Step-by-step explanation:

In one hour, the distance between them is reduced by 7+5 = 12 miles. At that rate, the 18 mile distance between them will be reduced to zero in ...

  time = distance/speed

  time = (18 mi)/(12 mi/h) = 3/2 h

It will take 1 1/2 hours until Mort and George meet.

if 9/24 equals 3/x , then x is ____​

Answers

[tex]\\ \sf\longmapsto \dfrac{9}{24}=\dfrac{3}{x}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{8}=\dfrac{3}{x}[/tex]

[tex]\\ \sf\longmapsto 3x=24[/tex]

[tex]\\ \sf\longmapsto x=24/3[/tex]

[tex]\\ \sf\longmapsto x=8[/tex]

1 2/15 + -3 1/2 in simplest form​

Answers

1 2/15 + -3 1/2

17/15 - 7/2

17/15 Multiply by (2) = 34/30

7/2 Multiply by (15) = 105/30
Subtract
34/30 - 105/30

-74/30

- 2 14/30 divide by 2 ( 7/15)

- 2 7/15

Pls i need an answer now ​

Answers

Answer:

Step-by-step explanation:

1. 5, 3.5, [tex]\sqrt{9\\}[/tex], [tex]-\frac{12}{5}[/tex], -7

2. 10, π ,3.1415, 0, -10

3. 1[tex]\frac{1}{2}[/tex], 1.44, 1.4(3), 1.(43), [tex]\frac{7}{5}[/tex]

solve using quadratic formula
3n^2-2n-5=0

Answers

=5/3   =−1

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

An object is launched directly in the air at a speed of 8 feet per second from a platform located 4 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+8t+4, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?

Answers

The maximum height is 68 ft. The easiest way to find this answer is by using the online desmos graphing calculator. It is a lifesaver

Does "greater than" sign and "not equal to" sign denote the same thing?​

Answers

Hello!

The "greater than sign" means one number is greater than the other.

Example: 4>2 (4 is greater than 2)

The "not equal to sign" means one number is not equal to another one.

Example: 15[tex]\neq[/tex]17 (15 is not equal to 17)

Hope this helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

no they dont

greater than sign denotes that the first digit is greater than the other digit

If x = 5-2√6, find the value of:
(i) x + 1/x
(ii) x² + 1/x²
Please solve ASAP​

Answers

Answer:

x+(1/x) = 10 and x²+ (1/x²) = 98

Step-by-step explanation:

Given that :

x = 5-2√6

1/x = 1/(5-2√6)

The denominator = 5-2√6

The Rationalising factor of 5-2√6 = 5+2√6

On Rationalising the denominator then

⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]

⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]

⇛ 1/x = (5+2√6)/[5²-(2√6)²]

Since (a+b)(a-b) = a²-b²

Where ,

a = 5 and b = 2√6

⇛1/x = (5+2√6)/(25-24)

⇛ 1/x = (5+2√6)/1

⇛ 1/x = 5+2√6

Now,

x +(1/x)

⇛ 5-2√6+5+2√6

⇛ 5+5

⇛ 10

Therefore, x+(1/x) = 10.

On squaring both sides then

⇛ [x+(1/x)]² = 10²

⇛ x²+2(x)(1/x)+(1/x)² =100

⇛ x²+2+(1/x)² = 100

⇛ x²+(1/x²) = 100-2

⇛ x²+(1/x²) = 98

Therefore, x²+(1/x²) = 98.

Read more:

Similar questions;

Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....

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